What it means
Most risk measures, such as standard deviation, treat upward and downward moves alike. An investor, though, does not mind a big gain, and what causes worry is a loss from a previous high, which is called a drawdown.
The Ulcer Index captures only that downside. It looks at the percentage drawdown at each point in time, squares it, averages the results and takes the square root, so deep and long-lasting falls count heavily.
Because it measures both depth and duration, an investment that sinks 20% and stays there for a year scores much worse than one that dips 20% for a day and then recovers. This matches how real investors feel, since a long wait to get back to a previous high is painful.
A lower Ulcer Index means a smoother path with smaller or shorter drawdowns. Analysts use it to compare funds that have similar returns but different experiences along the way.
It is also used in a performance ratio, sometimes called the Martin ratio or Ulcer Performance Index, which divides the return above the risk-free rate by the Ulcer Index. This shows how much return was earned per unit of drawdown stress.
Like any statistic based on past data, the index depends on the period chosen and says nothing certain about the future. It is best used alongside other measures, such as maximum drawdown and the Sharpe ratio.
In practice
Real-world examples.
Example
A financial adviser compares two funds that both returned 8% a year over five years. Fund A has an Ulcer Index of 3, and Fund B has an Ulcer Index of 9. She recommends Fund A to a nervous client because it spent less time and depth below its highs. She explains that the client is more likely to stay invested through a downturn if the ride is smoother.
Example
A pension trustee reviews three investment managers. One has a strong return but an Ulcer Index far above the others, since it endured a long, deep decline in a downturn. The trustee asks the manager to explain what happened and whether it could be repeated. The manager shows how the portfolio was repositioned after the decline, and the trustees record the discussion in their minutes.
Example
A private investor tracks her own portfolio monthly. When her Ulcer Index rises from 4 to 8 during a market fall, she uses it as a prompt to check that her risk level still matches her comfort. She decides to hold more cash so that a fall does not force her to sell.
Formula
Calculation
Percentage drawdown at each period = (price - highest price so far) / highest price so far x 100
Ulcer Index = square root of (sum of squared percentage drawdowns / number of periods)
An investment has the following month-end values over eight months: $250, $250, $220, $220, $250, $250, $250, $250.
The highest price so far is $250 throughout. In months 3 and 4, the drawdown is (220 - 250) / 250 x 100 = -12%. In all other months, the drawdown is 0%.
Sum of squared drawdowns = 12 x 12 + 12 x 12 = 144 + 144 = 288.
Average = 288 / 8 = 36.
Ulcer Index = square root of 36 = 6.
The Ulcer Index is 6, meaning that a typical investor's discomfort is equivalent to a drawdown of about 6%.Case study
Seen in the real world.
Westvale Capital is a fictional asset manager used for this illustrative example. It offered two strategies with the same average annual return of 7%, a growth strategy and a cautious one.
When the firm calculated the Ulcer Index over ten years, the growth strategy scored 11, because it had spent two long periods well below its peaks, while the cautious strategy scored 4. Standard deviation had suggested the two were closer together than they felt to clients.
The firm included the Ulcer Index in client reports, explaining it in plain terms as a measure of stress from falls. Several clients with short time horizons moved into the cautious strategy. The illustrative lesson is that the Ulcer Index tells a story that a headline return does not. The firm also noted that the measure is only as good as the data window, so it refreshed the figures every quarter.
Watch out
Common mistakes.
- Treating a low Ulcer Index as a guarantee of safety. It describes past drawdowns and cannot rule out future losses.
- Comparing indexes calculated over different periods or frequencies. Daily, weekly and monthly data give different results, so match them.
- Confusing it with standard deviation. The Ulcer Index looks only at declines from a previous peak, whereas standard deviation counts all fluctuations.
Questions
People also ask.
Why is it called the Ulcer Index?
The name reflects the stress and discomfort investors feel when a portfolio stays below its previous high for a long time.
What is a good Ulcer Index?
There is no universal cut-off. Lower is better, and it is most useful for comparing similar investments over the same period.
How is it different from maximum drawdown?
Maximum drawdown records only the single worst fall, while the Ulcer Index also reflects how long and how often the investment was below its peak.
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